nalgebra_sparse/

proptest.rs

//! Functionality for integrating `nalgebra-sparse` with `proptest`.
//!
//! **This module is only available if the `proptest-support` feature is enabled**.
//!
//! The strategies provided here are generally expected to be able to generate the entire range
//! of possible outputs given the constraints on dimensions and values. However, there are no
//! particular guarantees on the distribution of possible values.
use crate::coo::CooMatrix;
use crate::csc::CscMatrix;
use crate::csr::CsrMatrix;
use crate::pattern::SparsityPattern;
use nalgebra::proptest::DimRange;
use nalgebra::{Dim, Scalar};
use proptest::collection::{btree_set, hash_map, vec};
use proptest::prelude::*;
use proptest::sample::Index;
use std::cmp::min;
use std::iter::repeat;

fn dense_row_major_coord_strategy(
    nrows: usize,
    ncols: usize,
    nnz: usize,
) -> impl Strategy<Value = Vec<(usize, usize)>> {
    assert!(nnz <= nrows * ncols);
    let mut booleans = vec![true; nnz];
    booleans.append(&mut vec![false; (nrows * ncols) - nnz]);
    // Make sure that exactly `nnz` of the booleans are true
    Just(booleans)
        // Need to shuffle to make sure they are randomly distributed
        .prop_shuffle()
        .prop_map(move |booleans| {
        booleans
            .into_iter()
            .enumerate()
            .filter_map(|(index, is_entry)| {
                if is_entry {
                    // Convert linear index to row/col pair
                    let i = index / ncols;
                    let j = index % ncols;
                    Some((i, j))
                } else {
                    None
                }
            })
            .collect::<Vec<_>>()
    })
}

/// A strategy for generating `nnz` triplets.
///
/// This strategy should generally only be used when `nnz` is close to `nrows * ncols`.
fn dense_triplet_strategy<T>(
    value_strategy: T,
    nrows: usize,
    ncols: usize,
    nnz: usize,
) -> impl Strategy<Value = Vec<(usize, usize, T::Value)>>
where
    T: Strategy + Clone + 'static,
    T::Value: Scalar,
{
    assert!(nnz <= nrows * ncols);

    // Construct a number of booleans of which exactly `nnz` are true.
    let booleans: Vec<_> = repeat(true)
        .take(nnz)
        .chain(repeat(false))
        .take(nrows * ncols)
        .collect();

    Just(booleans)
        // Shuffle the booleans so that they are randomly distributed
        .prop_shuffle()
        // Convert the booleans into a list of coordinate pairs
        .prop_map(move |booleans| {
            booleans
                .into_iter()
                .enumerate()
                .filter_map(|(index, is_entry)| {
                    if is_entry {
                        // Convert linear index to row/col pair
                        let i = index / ncols;
                        let j = index % ncols;
                        Some((i, j))
                    } else {
                        None
                    }
                })
                .collect::<Vec<_>>()
        })
        // Assign values to each coordinate pair in order to generate a list of triplets
        .prop_flat_map(move |coords| {
            vec![value_strategy.clone(); coords.len()].prop_map(move |values| {
                coords
                    .clone()
                    .into_iter()
                    .zip(values)
                    .map(|((i, j), v)| (i, j, v))
                    .collect::<Vec<_>>()
            })
        })
}

/// A strategy for generating `nnz` triplets.
///
/// This strategy should generally only be used when `nnz << nrows * ncols`. If `nnz` is too
/// close to `nrows * ncols` it may fail due to excessive rejected samples.
fn sparse_triplet_strategy<T>(
    value_strategy: T,
    nrows: usize,
    ncols: usize,
    nnz: usize,
) -> impl Strategy<Value = Vec<(usize, usize, T::Value)>>
where
    T: Strategy + Clone + 'static,
    T::Value: Scalar,
{
    // Have to handle the zero case: proptest doesn't like empty ranges (i.e. 0 .. 0)
    let row_index_strategy = if nrows > 0 { 0..nrows } else { 0..1 };
    let col_index_strategy = if ncols > 0 { 0..ncols } else { 0..1 };
    let coord_strategy = (row_index_strategy, col_index_strategy);
    hash_map(coord_strategy, value_strategy.clone(), nnz)
        .prop_map(|hash_map| {
            let triplets: Vec<_> = hash_map.into_iter().map(|((i, j), v)| (i, j, v)).collect();
            triplets
        })
        // Although order in the hash map is unspecified, it's not necessarily *random*
        // - or, in particular, it does not necessarily sample the whole space of possible outcomes -
        // so we additionally shuffle the triplets
        .prop_shuffle()
}

/// A strategy for producing COO matrices without duplicate entries.
///
/// The values of the matrix are picked from the provided `value_strategy`, while the size of the
/// generated matrices is determined by the ranges `rows` and `cols`. The number of explicitly
/// stored entries is bounded from above by `max_nonzeros`. Note that the matrix might still
/// contain explicitly stored zeroes if the value strategy is capable of generating zero values.
pub fn coo_no_duplicates<T>(
    value_strategy: T,
    rows: impl Into<DimRange>,
    cols: impl Into<DimRange>,
    max_nonzeros: usize,
) -> impl Strategy<Value = CooMatrix<T::Value>>
where
    T: Strategy + Clone + 'static,
    T::Value: Scalar,
{
    (
        rows.into().to_range_inclusive(),
        cols.into().to_range_inclusive(),
    )
        .prop_flat_map(move |(nrows, ncols)| {
            let max_nonzeros = min(max_nonzeros, nrows * ncols);
            let size_range = 0..=max_nonzeros;
            let value_strategy = value_strategy.clone();

            size_range
                .prop_flat_map(move |nnz| {
                    let value_strategy = value_strategy.clone();
                    if nnz as f64 > 0.10 * (nrows as f64) * (ncols as f64) {
                        // If the number of nnz is sufficiently dense, then use the dense
                        // sample strategy
                        dense_triplet_strategy(value_strategy, nrows, ncols, nnz).boxed()
                    } else {
                        // Otherwise, use a hash map strategy so that we can get a sparse sampling
                        // (so that complexity is rather on the order of max_nnz than nrows * ncols)
                        sparse_triplet_strategy(value_strategy, nrows, ncols, nnz).boxed()
                    }
                })
                .prop_map(move |triplets| {
                    let mut coo = CooMatrix::new(nrows, ncols);
                    for (i, j, v) in triplets {
                        coo.push(i, j, v);
                    }
                    coo
                })
        })
}

/// A strategy for producing COO matrices with duplicate entries.
///
/// The values of the matrix are picked from the provided `value_strategy`, while the size of the
/// generated matrices is determined by the ranges `rows` and `cols`. Note that the values
/// only apply to individual entries, and since this strategy can generate duplicate entries,
/// the matrix will generally have values outside the range determined by `value_strategy` when
/// converted to other formats, since the duplicate entries are summed together in this case.
///
/// The number of explicitly stored entries is bounded from above by `max_nonzeros`. The maximum
/// number of duplicate entries is determined by `max_duplicates`. Note that the matrix might still
/// contain explicitly stored zeroes if the value strategy is capable of generating zero values.
pub fn coo_with_duplicates<T>(
    value_strategy: T,
    rows: impl Into<DimRange>,
    cols: impl Into<DimRange>,
    max_nonzeros: usize,
    max_duplicates: usize,
) -> impl Strategy<Value = CooMatrix<T::Value>>
where
    T: Strategy + Clone + 'static,
    T::Value: Scalar,
{
    let coo_strategy = coo_no_duplicates(value_strategy.clone(), rows, cols, max_nonzeros);
    let duplicate_strategy = vec((any::<Index>(), value_strategy.clone()), 0..=max_duplicates);
    (coo_strategy, duplicate_strategy)
        .prop_flat_map(|(coo, duplicates)| {
            let mut triplets: Vec<(usize, usize, T::Value)> = coo
                .triplet_iter()
                .map(|(i, j, v)| (i, j, v.clone()))
                .collect();
            if !triplets.is_empty() {
                let duplicates_iter: Vec<_> = duplicates
                    .into_iter()
                    .map(|(idx, val)| {
                        let (i, j, _) = idx.get(&triplets);
                        (*i, *j, val)
                    })
                    .collect();
                triplets.extend(duplicates_iter);
            }
            // Make sure to shuffle so that the duplicates get mixed in with the non-duplicates
            let shuffled = Just(triplets).prop_shuffle();
            (Just(coo.nrows()), Just(coo.ncols()), shuffled)
        })
        .prop_map(move |(nrows, ncols, triplets)| {
            let mut coo = CooMatrix::new(nrows, ncols);
            for (i, j, v) in triplets {
                coo.push(i, j, v);
            }
            coo
        })
}

fn sparsity_pattern_from_row_major_coords<I>(
    nmajor: usize,
    nminor: usize,
    coords: I,
) -> SparsityPattern
where
    I: Iterator<Item = (usize, usize)> + ExactSizeIterator,
{
    let mut minors = Vec::with_capacity(coords.len());
    let mut offsets = Vec::with_capacity(nmajor + 1);
    let mut current_major = 0;
    offsets.push(0);
    for (idx, (i, j)) in coords.enumerate() {
        assert!(i >= current_major);
        assert!(
            i < nmajor && j < nminor,
            "Generated coords are out of bounds"
        );
        while current_major < i {
            offsets.push(idx);
            current_major += 1;
        }
        minors.push(j);
    }

    while current_major < nmajor {
        offsets.push(minors.len());
        current_major += 1;
    }

    assert_eq!(offsets.first().unwrap(), &0);
    assert_eq!(offsets.len(), nmajor + 1);

    SparsityPattern::try_from_offsets_and_indices(nmajor, nminor, offsets, minors)
        .expect("Internal error: Generated sparsity pattern is invalid")
}

/// A strategy for generating sparsity patterns.
pub fn sparsity_pattern(
    major_lanes: impl Into<DimRange>,
    minor_lanes: impl Into<DimRange>,
    max_nonzeros: usize,
) -> impl Strategy<Value = SparsityPattern> {
    (
        major_lanes.into().to_range_inclusive(),
        minor_lanes.into().to_range_inclusive(),
    )
        .prop_flat_map(move |(nmajor, nminor)| {
            let max_nonzeros = min(nmajor * nminor, max_nonzeros);
            (Just(nmajor), Just(nminor), 0..=max_nonzeros)
        })
        .prop_flat_map(move |(nmajor, nminor, nnz)| {
            if 10 * nnz < nmajor * nminor {
                // If nnz is small compared to a dense matrix, then use a sparse sampling strategy
                btree_set((0..nmajor, 0..nminor), nnz)
                    .prop_map(move |coords| {
                        sparsity_pattern_from_row_major_coords(nmajor, nminor, coords.into_iter())
                    })
                    .boxed()
            } else {
                // If the required number of nonzeros is sufficiently dense,
                // we instead use a dense sampling
                dense_row_major_coord_strategy(nmajor, nminor, nnz)
                    .prop_map(move |coords| {
                        let coords = coords.into_iter();
                        sparsity_pattern_from_row_major_coords(nmajor, nminor, coords)
                    })
                    .boxed()
            }
        })
}

/// A strategy for generating CSR matrices.
pub fn csr<T>(
    value_strategy: T,
    rows: impl Into<DimRange>,
    cols: impl Into<DimRange>,
    max_nonzeros: usize,
) -> impl Strategy<Value = CsrMatrix<T::Value>>
where
    T: Strategy + Clone + 'static,
    T::Value: Scalar,
{
    let rows = rows.into();
    let cols = cols.into();
    sparsity_pattern(
        rows.lower_bound().value()..=rows.upper_bound().value(),
        cols.lower_bound().value()..=cols.upper_bound().value(),
        max_nonzeros,
    )
    .prop_flat_map(move |pattern| {
        let nnz = pattern.nnz();
        let values = vec![value_strategy.clone(); nnz];
        (Just(pattern), values)
    })
    .prop_map(|(pattern, values)| {
        CsrMatrix::try_from_pattern_and_values(pattern, values)
            .expect("Internal error: Generated CsrMatrix is invalid")
    })
}

/// A strategy for generating CSC matrices.
pub fn csc<T>(
    value_strategy: T,
    rows: impl Into<DimRange>,
    cols: impl Into<DimRange>,
    max_nonzeros: usize,
) -> impl Strategy<Value = CscMatrix<T::Value>>
where
    T: Strategy + Clone + 'static,
    T::Value: Scalar,
{
    let rows = rows.into();
    let cols = cols.into();
    sparsity_pattern(
        cols.lower_bound().value()..=cols.upper_bound().value(),
        rows.lower_bound().value()..=rows.upper_bound().value(),
        max_nonzeros,
    )
    .prop_flat_map(move |pattern| {
        let nnz = pattern.nnz();
        let values = vec![value_strategy.clone(); nnz];
        (Just(pattern), values)
    })
    .prop_map(|(pattern, values)| {
        CscMatrix::try_from_pattern_and_values(pattern, values)
            .expect("Internal error: Generated CscMatrix is invalid")
    })
}